Portable working machines of the above defined type are known since long. They are often used for cutting concrete and similar materials. The cutting creates a lot of abrasive dust. Without air filtration the engine will wear out in less than half an hour of operation. Efficient filters are therefore vital and are attained mainly through a big filter volume. An increased filter volume will increase the service life of the machine. For example, a machine of this type is described in U.S. Pat. No. 5,438,965. This machine, its precursors and successors, belonging to the applicant's “Partner® K650-family”, and variants of it, have been and are still widely used in the construction industry for cutting concrete and the like, and also by fire brigades for cutting holes in roofings or for penetrating vehicle wrecks, and similar tasks. It has a rear handle protruding backwards from the machine unit. This ensures a long distance between front and rear handles enabling a comfortable and precise control of the machine. This is an advantage compared to a similar type of machine that instead has its rear handle protruding upwards from the machine unit and therefore has a much shorter distance between the handles. However the machine described in U.S. Pat. No. 5,438,965 also has some shortcomings, which mainly have to do with a traditional thinking as far as the general layout of the machine unit is concerned. For example, the engine cylinder with its bore is conventionally inclined somewhat rearwards relative to a base line of the entire machine and/or to the bottom of the machine unit. This tends to limit the available space for other important components of the machine unit, such as an assembly which comprises members for supplying air and fuel to the engine, including a carburetor and a filter system for a given overall machine length. This in turn restricts the possibilities to give the said components an appropriate design and shape.